Floating UI window in 3D view
For a floating panel that stays in place you might want to read this question.

For something closer to the operator properties panel you could define a custom draw method to send to custom popup menu.

def draw_popup(self, context):
    col = self.layout.column()
    row = col.row()
    row.label("Hello World")
    row = col.row()
    row.prop(context.scene.render, 'resolution_x')

class ShowPopupOperator(bpy.types.Operator):
    bl_idname = "object.show_popup"
    bl_label = "sample show popup"

    def invoke(self, context, event):
        context.window_manager.popup_menu(draw_popup, title='Test this', icon='INFO')
        return {'FINISHED'}


To show the operator properties as shown in your question you can use the invoke_props_popup. To customise the display you give your operator a draw method.

class ShowPopupOperator(bpy.types.Operator):
    bl_idname = "object.show_popup"
    bl_label = "sample show popup"
    bl_options = {'REGISTER','UNDO'}

    prop1 = bpy.props.IntProperty()
    prop2 = bpy.props.FloatProperty()

    def invoke(self, context, event):
        return context.window_manager.invoke_props_popup(self, event)

    def execute(self, context):
        # do stuff here
        return {'FINISHED'}

    def draw(self, context):
        col = self.layout.column()
        row = col.row()
        row.label("Hello this the operator drawing")
        row = col.row()
        row.prop(self, 'prop1')
        row = col.row()
        row.prop(self, 'prop2')